Question

How to find answer for if a^7=7777 and a^6/b=11, what is the value of ab?

Answer 1

`\bf \begin{cases} a^7=7777\\\\ \cfrac{a^6}{b}=11 \end{cases} \\\\ -------------------------------\\\\ a^7\iff a^6a^1=7777\implies \begin{cases} a^6=(7777)/(a)\\\\ a=(7777)/(a^6) \end{cases}\\\\ -------------------------------\\\\ \cfrac{a^6}{b}=11\implies \cfrac{a^6}{11}=b\implies \cfrac{(7777)/(a)}{11}=b\implies \cfrac{7777}{a}\cdot \cfrac{1}{11}=b \\\\\\ \cfrac{707}{a}=b\\\\ -------------------------------\\\\`


`\bf a\cdot b=\cfrac{7777}{a^6}\cdot \cfrac{707}{a}\implies ab=\cfrac{7777\cdot 707}{a^6a^1}\implies ab=\cfrac{7777\cdot 707}{a^7} \\\\\\ \textit{but we know }a^7=7777\qquad thus\implies ab=\cfrac{7777}{a^7}\cdot 707 \\\\\\ ab=\cfrac{7777}{7777}\cdot 707\implies ab=1\cdot 707\implies ab=707`

Answer 2

`ab=707`

Explanation:

Given that

`a^7=7777\\`

`a^6/b=11`

We have to find the value of ab

WE see that when we divide I equation by II equation we get ab

`(a^7)/((a^6)/(b) ) =(a^7b)/(a^6)`

by rule for reciprocals

Now use exponent rule for simplifying a terms

`a^(7-6) b =(7777)/(11) \\ab=707`